In a certain code, 'REACTION' is written as 'RAETCOIN'. How is 'BEAUTY'…

In this type of letter-coding puzzle, the code is generated by a positional rule applied to the source word: the first and last letters of the word stay fixed, while the letters in between are split into consecutive pairs (from left to right) and each pair has its two letters swapped internally.

1. Compare REACTION and its code RAETCOIN letter by letter to find the rule: the first and last letters, R and N, are unchanged.

2. The middle letters of REACTION — E-A-C-T-I-O — split into three consecutive pairs: EA, CT, IO.

3. Swapping each pair internally gives AE, TC, OI; placing them in order after R and before N gives R-AE-TC-OI-N = RAETCOIN, confirming the rule.

4. Apply the same rule to BEAUTY: keep B and Y fixed; the middle letters E-A-U-T form two pairs, EA and UT.

5. Swap each pair internally: EA becomes AE, UT becomes TU.

6. Assemble the result: B + AE + TU + Y = BAETUY.

• Reversing the whole middle segment instead of swapping adjacent pairs (EAUT → TUAE) gives BTUAEY, which breaks the pair-swap rule confirmed from REACTION.

• Swapping only the outer letters of the middle segment while leaving the inner two untouched (E and T swap, A and U stay) gives BTAUEY, which also breaks the confirmed pairwise-swap pattern.

• Since an arrangement matching the confirmed rule does exist among the given options, ‘none of these’ cannot be correct here.

So BEAUTY is coded as BAETUY.